If things vary, they are different from each other in size, amount, or degree.

What does with varying degrees of success mean?

@sa_ra_ “varying degrees of ...” Is a very common phrase. It means different amounts. So, some are successful, some are less successful. See a translation.

What is the synonym of degree?

level, stage, point, rung, standard, grade, gradation, mark. amount, extent, measure, magnitude, intensity, strength. proportion, ratio.